Show that `p(x)=x^3-3x^2+2x-6` has only one real zero

Find the value of such that x^(3)-|a|x^(2)+ 3x +4 = 0 has only one real root.

Let f(x)=x^3+2x^2+x+5. Show that f(x)=0 has only one real root alpha such that [alpha]=-3

Show that the equation x^(3)+2x^(2)+x+5=0 has only one real root, such that [alpha]=-3 , where [x] denotes the integral point of x

Prove that the equation 3x^(5)+15x -8=0 has only one real root .

If the equation x^(3)+px^(2)+qx+1=0(p

Prove that x^(6)+x^(4)+x^(2)+x+3=0 has no positive real roots.

Prove that the equation,3x^(3)-6x^(2)+6x+sin x=0 has exactly one real root.

Show that for any real numbers lambda, the polynomial P(x)=x^(7)+x^(3)+lambda, has exactly one real root.

If the equaion x^(2) + ax+ b = 0 has distinct real roots and x^(2) + a|x| +b = 0 has only one real root, then